Note that adding Firebase to your Unity project involves tasks both in the
Firebase console and in your open Unity project
(for example, you download Firebase config files from the console, then move
them into your Unity project).

Next Steps

After a user signs in for the first time, a new user account is created and
linked to the credentials—that is, the user name and password, phone
number, or auth provider information—the user signed in with. This new
account is stored as part of your Firebase project, and can be used to identify
a user across every app in your project, regardless of how the user signs in.